Abstract
This paper presents a mathematical model of blood pressure regulation described by a system of delay differential equations. The model incorporates two key physiological mechanisms - the baroreceptor and renal regulatory loops - each represented as control channels with distinct response times. The state variable is the mean systolic pressure, while the control actions are modelled through peripheral vascular resistance and renal fluid excretion rate. To ensure system stability, a finite-time stabilization (FTS) method is developed based on linear approximation and regression-based parameter identification using experimental data. The resulting system is solved numerically using the 4th-order Runge-Kutta method. The model's reliability is supported by statistical data provided by a cardiology institute, demonstrating its applicability for analyzing blood pressure dynamics under both physiological and pathological conditions.